lecture15aa - Lecture 2/22/08 Binding and Nonbinding...

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Lecture 2/22/08 Binding and Nonbinding Constraints Example of Minimization LP
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An Example LP Problem Blue Ridge Hot Tubs produces two types of hot tubs: Aqua-Spas & Hydro-Luxes. There are 200 pumps, 1566 hours of labor, and 2880 feet of tubing available. Aqua-Spa Hydro-Lux Pumps 1 1 Labor 9 hours 6 hours Tubing 12 feet 16 feet Unit Profit $350 $300
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Summary of the LP Model for Blue Ridge Hot Tubs MAX: 350X 1 + 300X 2 (Maximize Profit) S.T.: 1X 1 + 1X 2 200 (Pump Constraint) 9X 1 + 6X 2 1566 (Labor Constraint) 12X 1 + 16X 2 2880 (Tubing Constraint) X 1 0 X 2 0 Non-negativity Constraints
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Optimal Solution X 1 =122, X 2 =78 Total Profit = $350*122 + $300*78 = $66,100
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X 2 X 1 250 200 150 100 50 0 0 50 100 150 200 250 (0, 180 ) (174, 0) Enumerating The Corner Points (122, 78) (0, 0) obj. value = $54,000 obj. value = $64,000 obj. value = $66,100 obj. value = $60,900 obj. value = $0 Note: This technique will not work if the solution is unbounded. Pump constraint Labor constraint Tubing constraint
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Summary of Graphical Solution to LP Problems 1. Plot the boundary line of each constraint 2. Identify the feasible region 3. Locate the optimal solution by either: a. Plotting level curves b. Enumerating the extreme points
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lecture15aa - Lecture 2/22/08 Binding and Nonbinding...

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